goodyear2013 wrote:

Merry and Michelle play a card game. In the beginning of the game they have an equal number of cards. Each player, at her turn, gives the other a third of her cards. Michelle plays first, giving Merry a third of her cards. Merry plays next, and Michelle follows. Then the game ends. Merry ended up with 14 more cards than Michelle. How many cards did each player have originally?

A) 18

B) 27

C) 36

D) 45

E) 54

Official solution from The

Economist.

Numbers in the answer choices and a specific question ("...how many cards...") call for Plugging In The Answers. If you feel like writing down equations, or if you are stunned by a long convoluted story in the question, stop! These are stop signs for Reverse PI.

Assume the amount in the answer choice is the number of cards each players has in the beginning, and then follow the story in the problem. If everything fits - stop. Pick it. Otherwise - POE and move on, until you find an answer that works.

First, plug in answer choice C. Assume that each player had 36 cards in the beginning of the game. This is how the game proceeds:

Michelle Mary

Equal amounts 36 36

Michelle gives 1/3 · 36=12 cards to Mary 24 48

Mary gives 1/3 · 48=16 cards to Michelle 40 32

Michelle gives 1/3 · 40 cards to Mary 40-40/3 32+40/3

The last turn cannot be accomplished because a third of 40 cards is not an integer number. POE C, and look for another answer choice.

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